Finite Group DatabasebetaFinite Group Databasebeta| order | 32193 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C72×C73 ⋊ C32 |
| derived | C7×C73 ⋊ C32×C7 |
| Sylow | C73 ⋊ C3×C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C3×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | ΓL(1,𝔽8)×C73⋊C3 |
| commutator, cosocle, hypocenter | C7×C73 | C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C73 | C32 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C7 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1533 |
945 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32193, 29);